Question

Assertion (A) : For matrix A = [1 cos θ 1; – cos θ 1 cos θ; – 1 – cos θ 1], where θ ∈ [0, 2π], |A| ∈ [2, 4]. Reason (R) : cos θ ∈ [– 1, 1], ∀ θ ∈ [0, 2π].

If a function f : X → Y defined as f(x) = y is one-one and onto, then we can define a unique function g : Y → X such that g(y) = x, where x ∈ X and y = f(x), y ∈ Y. Function g is called the inverse of function f. The domain of sine function is R and function sine : R → R is neither one-one nor onto. The following graph shows the sine function. Let sine function be defined from set A to [– 1, 1] such that inverse of sine function exists, i.e., sin⁻¹ x is defined from [– 1, 1] to A. On the basis of the above information, answer the following questions :